L. Elisa Celis

Niclas Boehmer, L. Elisa Celis, Lingxiao Huang et al.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

L. Elisa Celis, Amit Kumar, Anay Mehrotra et al.

Biases with respect to socially-salient attributes of individuals have been well documented in evaluation processes used in settings such as admissions and hiring. We view such an evaluation process as a transformation of a distribution of the true utility of an individual for a task to an observed distribution and model it as a solution to a loss minimization problem subject to an information constraint. Our model has two parameters that have been identified as factors leading to biases: the resource-information trade-off parameter in the information constraint and the risk-averseness parameter in the loss function. We characterize the distributions that arise from our model and study the effect of the parameters on the observed distribution. The outputs of our model enrich the class of distributions that can be used to capture variation across groups in the observed evaluations. We empirically validate our model by fitting real-world datasets and use it to study the effect of interventions in a downstream selection task. These results contribute to an understanding of the emergence of bias in evaluation processes and provide tools to guide the deployment of interventions to mitigate biases.

L. Elisa Celis, Amit Kumar, Nisheeth K. Vishnoi et al.

This paper considers the scenario in which there are multiple institutions, each with a limited capacity for candidates, and candidates, each with preferences over the institutions. A central entity evaluates the utility of each candidate to the institutions, and the goal is to select candidates for each institution in a way that maximizes utility while also considering the candidates' preferences. The paper focuses on the setting in which candidates are divided into multiple groups and the observed utilities of candidates in some groups are biased--systematically lower than their true utilities. The first result is that, in these biased settings, prior algorithms can lead to selections with sub-optimal true utility and significant discrepancies in the fraction of candidates from each group that get their preferred choices. Subsequently, an algorithm is presented along with proof that it produces selections that achieve near-optimal group fairness with respect to preferences while also nearly maximizing the true utility under distributional assumptions. Further, extensive empirical validation of these results in real-world and synthetic settings, in which the distributional assumptions may not hold, are presented.

Vijay Keswani, L. Elisa Celis

In real-world classification settings, such as loan application evaluation or content moderation on online platforms, individuals respond to classifier predictions by strategically updating their features to increase their likelihood of receiving a particular (positive) decision (at a certain cost). Yet, when different demographic groups have different feature distributions or pay different update costs, prior work has shown that individuals from minority groups often pay a higher cost to update their features. Fair classification aims to address such classifier performance disparities by constraining the classifiers to satisfy statistical fairness properties. However, we show that standard fairness constraints do not guarantee that the constrained classifier reduces the disparity in strategic manipulation cost. To address such biases in strategic settings and provide equal opportunities for strategic manipulation, we propose a constrained optimization framework that constructs classifiers that lower the strategic manipulation cost for minority groups. We develop our framework by studying theoretical connections between group-specific strategic cost disparity and standard selection rate fairness metrics (e.g., statistical rate and true positive rate). Empirically, we show the efficacy of this approach over multiple real-world datasets.

Vijay Keswani, Anay Mehrotra, L. Elisa Celis

In many predictive contexts (e.g., credit lending), true outcomes are only observed for samples that were positively classified in the past. These past observations, in turn, form training datasets for classifiers that make future predictions. However, such training datasets lack information about the outcomes of samples that were (incorrectly) negatively classified in the past and can lead to erroneous classifiers. We present an approach that trains a classifier using available data and comes with a family of exploration strategies to collect outcome data about subpopulations that otherwise would have been ignored. For any exploration strategy, the approach comes with guarantees that (1) all sub-populations are explored, (2) the fraction of false positives is bounded, and (3) the trained classifier converges to a ``desired'' classifier. The right exploration strategy is context-dependent; it can be chosen to improve learning guarantees and encode context-specific group fairness properties. Evaluation on real-world datasets shows that this approach consistently boosts the quality of collected outcome data and improves the fraction of true positives for all groups, with only a small reduction in predictive utility.

L. Elisa Celis, Lingxiao Huang, Nisheeth K. Vishnoi

The rapid rise of Generative AI (GenAI) tools has sparked debate over their role in complementing or replacing human workers across job contexts. We present a mathematical framework that models jobs, workers, and worker-job fit, introducing a novel decomposition of skills into decision-level and action-level subskills to reflect the complementary strengths of humans and GenAI. We analyze how changes in subskill abilities affect job success, identifying conditions for sharp transitions in success probability. We also establish sufficient conditions under which combining workers with complementary subskills significantly outperforms relying on a single worker. This explains phenomena such as productivity compression, where GenAI assistance yields larger gains for lower-skilled workers. We demonstrate the framework' s practicality using data from O*NET and Big-Bench Lite, aligning real-world data with our model via subskill-division methods. Our results highlight when and how GenAI complements human skills, rather than replacing them.

L. Elisa Celis, Lingxiao Huang, Milind Sohoni et al.

Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort. Yet persistent disparities across race, gender, and class challenge this ideal. Some attribute these gaps to structural inequality; others to individual choice. We develop a game-theoretic model in which candidates from different socioeconomic groups differ in their perceived post-selection value--shaped by social context and, increasingly, by AI-powered tools offering personalized career or salary guidance. Each candidate strategically chooses effort, balancing its cost against expected reward; effort translates into observable merit, and selection is based solely on merit. We characterize the unique Nash equilibrium in the large-agent limit and derive explicit formulas showing how valuation disparities and institutional selectivity jointly determine effort, representation, social welfare, and utility. We further propose a cost-sensitive optimization framework that quantifies how modifying selectivity or perceived value can reduce disparities without compromising institutional goals. Our analysis reveals a perception-driven bias: when perceptions of post-selection value differ across groups, these differences translate into rational differences in effort, propagating disparities backward through otherwise "fair" selection processes. While the model is static, it captures one stage of a broader feedback cycle linking perceptions, incentives, and outcome--bridging rational-choice and structural explanations of inequality by showing how techno-social environments shape individual incentives in meritocratic systems.

Vijay Keswani, L. Elisa Celis, Krishnaram Kenthapadi et al.

Automatically assigning tasks to people is challenging because human performance can vary across tasks for many reasons. This challenge is further compounded in real-life settings in which no oracle exists to assess the quality of human decisions and task assignments made. Instead, we find ourselves in a "closed" decision-making loop in which the same fallible human decisions we rely on in practice must also be used to guide task allocation. How can imperfect and potentially biased human decisions train an accurate allocation model? Our key insight is to exploit weak prior information on human-task similarity to bootstrap model training. We show that the use of such a weak prior can improve task allocation accuracy, even when human decision-makers are fallible and biased. We present both theoretical analysis and empirical evaluation over synthetic data and a social media toxicity detection task. Results demonstrate the efficacy of our approach.

Vijay Keswani, L. Elisa Celis

Assessing the diversity of a dataset of information associated with people is crucial before using such data for downstream applications. For a given dataset, this often involves computing the imbalance or disparity in the empirical marginal distribution of a protected attribute (e.g. gender, dialect, etc.). However, real-world datasets, such as images from Google Search or collections of Twitter posts, often do not have protected attributes labeled. Consequently, to derive disparity measures for such datasets, the elements need to hand-labeled or crowd-annotated, which are expensive processes. We propose a cost-effective approach to approximate the disparity of a given unlabeled dataset, with respect to a protected attribute, using a control set of labeled representative examples. Our proposed algorithm uses the pairwise similarity between elements in the dataset and elements in the control set to effectively bootstrap an approximation to the disparity of the dataset. Importantly, we show that using a control set whose size is much smaller than the size of the dataset is sufficient to achieve a small approximation error. Further, based on our theoretical framework, we also provide an algorithm to construct adaptive control sets that achieve smaller approximation errors than randomly chosen control sets. Simulations on two image datasets and one Twitter dataset demonstrate the efficacy of our approach (using random and adaptive control sets) in auditing the diversity of a wide variety of datasets.

L. Elisa Celis, Anay Mehrotra, Nisheeth K. Vishnoi

We study fair classification in the presence of an omniscient adversary that, given an $η$, is allowed to choose an arbitrary $η$-fraction of the training samples and arbitrarily perturb their protected attributes. The motivation comes from settings in which protected attributes can be incorrect due to strategic misreporting, malicious actors, or errors in imputation; and prior approaches that make stochastic or independence assumptions on errors may not satisfy their guarantees in this adversarial setting. Our main contribution is an optimization framework to learn fair classifiers in this adversarial setting that comes with provable guarantees on accuracy and fairness. Our framework works with multiple and non-binary protected attributes, is designed for the large class of linear-fractional fairness metrics, and can also handle perturbations besides protected attributes. We prove near-tightness of our framework's guarantees for natural hypothesis classes: no algorithm can have significantly better accuracy and any algorithm with better fairness must have lower accuracy. Empirically, we evaluate the classifiers produced by our framework for statistical rate on real-world and synthetic datasets for a family of adversaries.

Anay Mehrotra, L. Elisa Celis

Subset selection algorithms are ubiquitous in AI-driven applications, including, online recruiting portals and image search engines, so it is imperative that these tools are not discriminatory on the basis of protected attributes such as gender or race. Currently, fair subset selection algorithms assume that the protected attributes are known as part of the dataset. However, protected attributes may be noisy due to errors during data collection or if they are imputed (as is often the case in real-world settings). While a wide body of work addresses the effect of noise on the performance of machine learning algorithms, its effect on fairness remains largely unexamined. We find that in the presence of noisy protected attributes, in attempting to increase fairness without considering noise, one can, in fact, decrease the fairness of the result! Towards addressing this, we consider an existing noise model in which there is probabilistic information about the protected attributes (e.g., [58, 34, 20, 46]), and ask is fair selection possible under noisy conditions? We formulate a ``denoised'' selection problem which functions for a large class of fairness metrics; given the desired fairness goal, the solution to the denoised problem violates the goal by at most a small multiplicative amount with high probability. Although this denoised problem turns out to be NP-hard, we give a linear-programming based approximation algorithm for it. We evaluate this approach on both synthetic and real-world datasets. Our empirical results show that this approach can produce subsets which significantly improve the fairness metrics despite the presence of noisy protected attributes, and, compared to prior noise-oblivious approaches, has better Pareto-tradeoffs between utility and fairness.

L. Elisa Celis, Chris Hays, Anay Mehrotra et al.

A robust body of evidence demonstrates the adverse effects of implicit bias in various contexts--from hiring to health care. The Rooney Rule is an intervention developed to counter implicit bias and has been implemented in the private and public sectors. The Rooney Rule requires that a selection panel include at least one candidate from an underrepresented group in their shortlist of candidates. Recently, Kleinberg and Raghavan proposed a model of implicit bias and studied the effectiveness of the Rooney Rule when applied to a single selection decision. However, selection decisions often occur repeatedly over time. Further, it has been observed that, given consistent counterstereotypical feedback, implicit biases against underrepresented candidates can change. We consider a model of how a selection panel's implicit bias changes over time given their hiring decisions either with or without the Rooney Rule in place. Our main result is that, when the panel is constrained by the Rooney Rule, their implicit bias roughly reduces at a rate that is the inverse of the size of the shortlist--independent of the number of candidates, whereas without the Rooney Rule, the rate is inversely proportional to the number of candidates. Thus, when the number of candidates is much larger than the size of the shortlist, the Rooney Rule enables a faster reduction in implicit bias, providing an additional reason in favor of using it as a strategy to mitigate implicit bias. Towards empirically evaluating the long-term effect of the Rooney Rule in repeated selection decisions, we conduct an iterative candidate selection experiment on Amazon MTurk. We observe that, indeed, decision-makers subject to the Rooney Rule select more minority candidates in addition to those required by the rule itself than they would if no rule is in effect, and do so without considerably decreasing the utility of candidates selected.

Vijay Keswani, L. Elisa Celis

Discussions on Twitter involve participation from different communities with different dialects and it is often necessary to summarize a large number of posts into a representative sample to provide a synopsis. Yet, any such representative sample should sufficiently portray the underlying dialect diversity to present the voices of different participating communities representing the dialects. Extractive summarization algorithms perform the task of constructing subsets that succinctly capture the topic of any given set of posts. However, we observe that there is dialect bias in the summaries generated by common summarization approaches, i.e., they often return summaries that under-represent certain dialects. The vast majority of existing "fair" summarization approaches require socially salient attribute labels (in this case, dialect) to ensure that the generated summary is fair with respect to the socially salient attribute. Nevertheless, in many applications, these labels do not exist. Furthermore, due to the ever-evolving nature of dialects in social media, it is unreasonable to label or accurately infer the dialect of every social media post. To correct for the dialect bias, we employ a framework that takes an existing text summarization algorithm as a blackbox and, using a small set of dialect-diverse sentences, returns a summary that is relatively more dialect-diverse. Crucially, this approach does not need the posts being summarized to have dialect labels, ensuring that the diversification process is independent of dialect classification/identification models. We show the efficacy of our approach on Twitter datasets containing posts written in dialects used by different social groups defined by race or gender; in all cases, our approach leads to improved dialect diversity compared to standard text summarization approaches.

L. Elisa Celis, Lingxiao Huang, Vijay Keswani et al.

We present an optimization framework for learning a fair classifier in the presence of noisy perturbations in the protected attributes. Compared to prior work, our framework can be employed with a very general class of linear and linear-fractional fairness constraints, can handle multiple, non-binary protected attributes, and outputs a classifier that comes with provable guarantees on both accuracy and fairness. Empirically, we show that our framework can be used to attain either statistical rate or false positive rate fairness guarantees with a minimal loss in accuracy, even when the noise is large, in two real-world datasets.

L. Elisa Celis, Anay Mehrotra, Nisheeth K. Vishnoi

Implicit bias is the unconscious attribution of particular qualities (or lack thereof) to a member from a particular social group (e.g., defined by gender or race). Studies on implicit bias have shown that these unconscious stereotypes can have adverse outcomes in various social contexts, such as job screening, teaching, or policing. Recently, (Kleinberg and Raghavan, 2018) considered a mathematical model for implicit bias and showed the effectiveness of the Rooney Rule as a constraint to improve the utility of the outcome for certain cases of the subset selection problem. Here we study the problem of designing interventions for the generalization of subset selection -- ranking -- that requires to output an ordered set and is a central primitive in various social and computational contexts. We present a family of simple and interpretable constraints and show that they can optimally mitigate implicit bias for a generalization of the model studied in (Kleinberg and Raghavan, 2018). Subsequently, we prove that under natural distributional assumptions on the utilities of items, simple, Rooney Rule-like, constraints can also surprisingly recover almost all the utility lost due to implicit biases. Finally, we augment our theoretical results with empirical findings on real-world distributions from the IIT-JEE (2009) dataset and the Semantic Scholar Research corpus.

Yi Chern Tan, L. Elisa Celis

Social bias in machine learning has drawn significant attention, with work ranging from demonstrations of bias in a multitude of applications, curating definitions of fairness for different contexts, to developing algorithms to mitigate bias. In natural language processing, gender bias has been shown to exist in context-free word embeddings. Recently, contextual word representations have outperformed word embeddings in several downstream NLP tasks. These word representations are conditioned on their context within a sentence, and can also be used to encode the entire sentence. In this paper, we analyze the extent to which state-of-the-art models for contextual word representations, such as BERT and GPT-2, encode biases with respect to gender, race, and intersectional identities. Towards this, we propose assessing bias at the contextual word level. This novel approach captures the contextual effects of bias missing in context-free word embeddings, yet avoids confounding effects that underestimate bias at the sentence encoding level. We demonstrate evidence of bias at the corpus level, find varying evidence of bias in embedding association tests, show in particular that racial bias is strongly encoded in contextual word models, and observe that bias effects for intersectional minorities are exacerbated beyond their constituent minority identities. Further, evaluating bias effects at the contextual word level captures biases that are not captured at the sentence level, confirming the need for our novel approach.

L. Elisa Celis, Vijay Keswani, Nisheeth K. Vishnoi

Data containing human or social attributes may over- or under-represent groups with respect to salient social attributes such as gender or race, which can lead to biases in downstream applications. This paper presents an algorithmic framework that can be used as a data preprocessing method towards mitigating such bias. Unlike prior work, it can efficiently learn distributions over large domains, controllably adjust the representation rates of protected groups and achieve target fairness metrics such as statistical parity, yet remains close to the empirical distribution induced by the given dataset. Our approach leverages the principle of maximum entropy - amongst all distributions satisfying a given set of constraints, we should choose the one closest in KL-divergence to a given prior. While maximum entropy distributions can succinctly encode distributions over large domains, they can be difficult to compute. Our main contribution is an instantiation of this framework for our set of constraints and priors, which encode our bias mitigation goals, and that runs in time polynomial in the dimension of the data. Empirically, we observe that samples from the learned distribution have desired representation rates and statistical rates, and when used for training a classifier incurs only a slight loss in accuracy while maintaining fairness properties.

L. Elisa Celis, Anay Mehrotra, Nisheeth K. Vishnoi

Online advertising platforms are thriving due to the customizable audiences they offer advertisers. However, recent studies show that advertisements can be discriminatory with respect to the gender or race of the audience that sees the ad, and may inadvertently cross ethical and/or legal boundaries. To prevent this, we propose a constrained ad auction framework that maximizes the platform's revenue conditioned on ensuring that the audience seeing an advertiser's ad is distributed appropriately across sensitive types such as gender or race. Building upon Myerson's classic work, we first present an optimal auction mechanism for a large class of fairness constraints. Finding the parameters of this optimal auction, however, turns out to be a non-convex problem. We show that this non-convex problem can be reformulated as a more structured non-convex problem with no saddle points or local-maxima; this allows us to develop a gradient-descent-based algorithm to solve it. Our empirical results on the A1 Yahoo! dataset demonstrate that our algorithm can obtain uniform coverage across different user types for each advertiser at a minor loss to the revenue of the platform, and a small change to the size of the audience each advertiser reaches.

L. Elisa Celis, Vijay Keswani

Motivated by concerns that machine learning algorithms may introduce significant bias in classification models, developing fair classifiers has become an important problem in machine learning research. One important paradigm towards this has been providing algorithms for adversarially learning fair classifiers (Zhang et al., 2018; Madras et al., 2018). We formulate the adversarial learning problem as a multi-objective optimization problem and find the fair model using gradient descent-ascent algorithm with a modified gradient update step, inspired by the approach of Zhang et al., 2018. We provide theoretical insight and guarantees that formalize the heuristic arguments presented previously towards taking such an approach. We test our approach empirically on the Adult dataset and synthetic datasets and compare against state of the art algorithms (Celis et al., 2018; Zhang et al., 2018; Zafar et al., 2017). The results show that our models and algorithms have comparable or better accuracy than other algorithms while performing better in terms of fairness, as measured using statistical rate or false discovery rate.

L. Elisa Celis, Vijay Keswani

Studies have shown that the people depicted in image search results tend to be of majority groups with respect to socially salient attributes. This skew goes beyond that which already exists in the world - e.g., Kay et al. showed that although 28% of CEOs in US are women, only 10% of the top 100 results for CEO in Google Image Search are women. Most existing approaches to correct for this kind of bias assume that the images of people include socially salient attribute labels. However, such labels are often unknown. Further, using automated techniques to infer these labels may often not be possible within acceptable accuracy ranges, and may not be desirable due to the additional biases this process could incur. We develop a novel approach that takes as input a visibly diverse control set of images and uses this set to select a set of images of people in response to a query. The goal is to have a resulting set that is more visibly diverse in a manner that emulates the diversity depicted in the control set. Importantly, this approach does not require images to be labelled at any point; effectively, it gives a way to implicitly diversify the set of images selected. We provide two variants of our approach: the first is a modification of the MMR algorithm to incorporate the diversity scores, and second is a more efficient variant that does not consider within-list redundancy. We evaluate these approaches empirically on two datasets 1) a new dataset containing top Google image results for 96 occupations, for which we evaluate gender and skin-tone diversity with respect to occupations and 2) the CelebA dataset for which we evaluate gender diversity with respect to facial features. Our approaches produce image sets that significantly improve the visible diversity of the results, compared to current Google search and other diverse image summarization algorithms, at a minimal cost to accuracy.

Sayash Kapoor, Vijay Keswani, Nisheeth K. Vishnoi et al.

We present a prototype for a news search engine that presents balanced viewpoints across liberal and conservative articles with the goal of de-polarizing content and allowing users to escape their filter bubble. The balancing is done according to flexible user-defined constraints, and leverages recent advances in constrained bandit optimization. We showcase our balanced news feed by displaying it side-by-side with the news feed produced by a traditional (polarized) feed.

L. Elisa Celis, Lingxiao Huang, Vijay Keswani et al.

Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works have focused on fairness with respect to a specific metric, modeled the corresponding fair classification problem as a constrained optimization problem, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which we do not have fair classifiers and many of the aforementioned algorithms do not come with theoretical guarantees; perhaps because the resulting optimization problem is non-convex. The main contribution of this paper is a new meta-algorithm for classification that takes as input a large class of fairness constraints, with respect to multiple non-disjoint sensitive attributes, and which comes with provable guarantees. This is achieved by first developing a meta-algorithm for a large family of classification problems with convex constraints, and then showing that classification problems with general types of fairness constraints can be reduced to those in this family. We present empirical results that show that our algorithm can achieve near-perfect fairness with respect to various fairness metrics, and that the loss in accuracy due to the imposed fairness constraints is often small. Overall, this work unifies several prior works on fair classification, presents a practical algorithm with theoretical guarantees, and can handle fairness metrics that were previously not possible.

L. Elisa Celis, Sayash Kapoor, Farnood Salehi et al.

Personalization is pervasive in the online space as it leads to higher efficiency and revenue by allowing the most relevant content to be served to each user. However, recent studies suggest that personalization methods can propagate societal or systemic biases and polarize opinions; this has led to calls for regulatory mechanisms and algorithms to combat bias and inequality. Algorithmically, bandit optimization has enjoyed great success in learning user preferences and personalizing content or feeds accordingly. We propose an algorithmic framework that allows for the possibility to control bias or discrimination in such bandit-based personalization. Our model allows for the specification of general fairness constraints on the sensitive types of the content that can be displayed to a user. The challenge, however, is to come up with a scalable and low regret algorithm for the constrained optimization problem that arises. Our main technical contribution is a provably fast and low-regret algorithm for the fairness-constrained bandit optimization problem. Our proofs crucially leverage the special structure of our problem. Experiments on synthetic and real-world data sets show that our algorithmic framework can control bias with only a minor loss to revenue.

L. Elisa Celis, Vijay Keswani, Damian Straszak et al.

Sampling methods that choose a subset of the data proportional to its diversity in the feature space are popular for data summarization. However, recent studies have noted the occurrence of bias (under- or over-representation of a certain gender or race) in such data summarization methods. In this paper we initiate a study of the problem of outputting a diverse and fair summary of a given dataset. We work with a well-studied determinantal measure of diversity and corresponding distributions (DPPs) and present a framework that allows us to incorporate a general class of fairness constraints into such distributions. Coming up with efficient algorithms to sample from these constrained determinantal distributions, however, suffers from a complexity barrier and we present a fast sampler that is provably good when the input vectors satisfy a natural property. Our experimental results on a real-world and an image dataset show that the diversity of the samples produced by adding fairness constraints is not too far from the unconstrained case, and we also provide a theoretical explanation of it.

Farnood Salehi, Patrick Thiran, L. Elisa Celis

Coordinate descent methods usually minimize a cost function by updating a random decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest decrease in the cost function. However, finding this coordinate would require checking all of them, which would effectively negate the improvement in computational tractability that coordinate descent is intended to afford. To address this, we propose a new adaptive method for selecting a coordinate. First, we find a lower bound on the amount the cost function decreases when a coordinate is updated. We then use a multi-armed bandit algorithm to learn which coordinates result in the largest lower bound by interleaving this learning with conventional coordinate descent updates except that the coordinate is selected proportionately to the expected decrease. We show that our approach improves the convergence of coordinate descent methods both theoretically and experimentally.

L. Elisa Celis, Lingxiao Huang, Nisheeth K. Vishnoi

Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting a committee), or specified types such as political leaning (when selecting a subset of news items), an algorithm that chooses a subset by optimizing a multiwinner voting rule may be unbalanced in its selection -- it may under or over represent a particular gender or political orientation in the examples above. We introduce an algorithmic framework for multiwinner voting problems when there is an additional requirement that the selected subset should be "fair" with respect to a given set of attributes. Our framework provides the flexibility to (1) specify fairness with respect to multiple, non-disjoint attributes (e.g., ethnicity and gender) and (2) specify a score function. We study the computational complexity of this constrained multiwinner voting problem for monotone and submodular score functions and present several approximation algorithms and matching hardness of approximation results for various attribute group structure and types of score functions. We also present simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case.

Farnood Salehi, L. Elisa Celis, Patrick Thiran

Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertently slows down the convergence rate of the algorithms. One way to reduce this variance is to sample the datapoints from a carefully selected non-uniform distribution. In this work, we propose a novel non-uniform sampling approach that uses the multi-armed bandit framework. Theoretically, we show that our algorithm asymptotically approximates the optimal variance within a factor of 3. Empirically, we show that using this datapoint-selection technique results in a significant reduction in the convergence time and variance of several stochastic optimization algorithms such as SGD, SVRG and SAGA. This approach for sampling datapoints is general, and can be used in conjunction with any algorithm that uses an unbiased gradient estimation -- we expect it to have broad applicability beyond the specific examples explored in this work.

L. Elisa Celis, Nisheeth K. Vishnoi

Personalization is pervasive in the online space as, when combined with learning, it leads to higher efficiency and revenue by allowing the most relevant content to be served to each user. However, recent studies suggest that such personalization can propagate societal or systemic biases, which has led to calls for regulatory mechanisms and algorithms to combat inequality. Here we propose a rigorous algorithmic framework that allows for the possibility to control biased or discriminatory personalization with respect to sensitive attributes of users without losing all of the benefits of personalization.

L. Elisa Celis, Peter M. Krafft, Nisheeth K. Vishnoi

We study a distributed learning process observed in human groups and other social animals. This learning process appears in settings in which each individual in a group is trying to decide over time, in a distributed manner, which option to select among a shared set of options. Specifically, we consider a stochastic dynamics in a group in which every individual selects an option in the following two-step process: (1) select a random individual and observe the option that individual chose in the previous time step, and (2) adopt that option if its stochastic quality was good at that time step. Various instantiations of such distributed learning appear in nature, and have also been studied in the social science literature. From the perspective of an individual, an attractive feature of this learning process is that it is a simple heuristic that requires extremely limited computational capacities. But what does it mean for the group -- could such a simple, distributed and essentially memoryless process lead the group as a whole to perform optimally? We show that the answer to this question is yes -- this distributed learning is highly effective at identifying the best option and is close to optimal for the group overall. Our analysis also gives quantitative bounds that show fast convergence of these stochastic dynamics. Prior to our work the only theoretical work related to such learning dynamics has been either in deterministic special cases or in the asymptotic setting. Finally, we observe that our infinite population dynamics is a stochastic variant of the classic multiplicative weights update (MWU) method. Consequently, we arrive at the following interesting converse: the learning dynamics on a finite population considered here can be viewed as a novel distributed and low-memory implementation of the classic MWU method.

L. Elisa Celis, Damian Straszak, Nisheeth K. Vishnoi

Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can result in decreased diversity in the type of content presented, promote stereotypes, and polarize opinions. In order to address such issues, we study the following variant of the traditional ranking problem when, in addition, there are fairness or diversity constraints. Given a collection of items along with 1) the value of placing an item in a particular position in the ranking, 2) the collection of sensitive attributes (such as gender, race, political opinion) of each item and 3) a collection of constraints that, for each k, bound the number of items with each attribute that are allowed to appear in the top k positions of the ranking, the goal is to output a ranking that maximizes the value with respect to the original rank quality metric while respecting the constraints. This problem encapsulates various well-studied problems related to bipartite and hypergraph matching as special cases and turns out to be hard to approximate even with simple constraints. Our main technical contributions are fast exact and approximation algorithms along with complementary hardness results that, together, come close to settling the approximability of this constrained ranking maximization problem. Unlike prior work on the constrained matching problems, our algorithm runs in linear time, even when the number of constraints is large, its approximation ratio does not depend on the number of constraints, and it produces solutions with small constraint violations. Our results rely on insights about the constrained matching problem when the objective satisfies properties that appear in common ranking metrics such as Discounted Cumulative Gain, Spearman's rho or Bradley-Terry.

L. Elisa Celis, Farnood Salehi

An individual's decisions are often guided by those of his or her peers, i.e., neighbors in a social network. Presumably, being privy to the experiences of others aids in learning and decision making, but how much advantage does an individual gain by observing her neighbors? Such problems make appearances in sociology and economics and, in this paper, we present a novel model to capture such decision-making processes and appeal to the classical multi-armed bandit framework to analyze it. Each individual, in addition to her own actions, can observe the actions and rewards obtained by her neighbors, and can use all of this information in order to minimize her own regret. We provide algorithms for this setting, both for stochastic and adversarial bandits, and show that their regret smoothly interpolates between the regret in the classical bandit setting and that of the full-information setting as a function of the neighbors' exploration. In the stochastic setting the additional information must simply be incorporated into the usual estimation of the rewards, while in the adversarial setting this is attained by constructing a new unbiased estimator for the rewards and appropriately bounding the amount of additional information provided by the neighbors. These algorithms are optimal up to log factors; despite the fact that the agents act independently and selfishly, this implies that it is an approximate Nash equilibria for all agents to use our algorithms. Further, we show via empirical simulations that our algorithms, often significantly, outperform existing algorithms that one could apply to this setting.

L. Elisa Celis, Amit Deshpande, Tarun Kathuria et al.

Due to the recent cases of algorithmic bias in data-driven decision-making, machine learning methods are being put under the microscope in order to understand the root cause of these biases and how to correct them. Here, we consider a basic algorithmic task that is central in machine learning: subsampling from a large data set. Subsamples are used both as an end-goal in data summarization (where fairness could either be a legal, political or moral requirement) and to train algorithms (where biases in the samples are often a source of bias in the resulting model). Consequently, there is a growing effort to modify either the subsampling methods or the algorithms themselves in order to ensure fairness. However, in doing so, a question that seems to be overlooked is whether it is possible to produce fair subsamples that are also adequately representative of the feature space of the data set - an important and classic requirement in machine learning. Can diversity and fairness be simultaneously ensured? We start by noting that, in some applications, guaranteeing one does not necessarily guarantee the other, and a new approach is required. Subsequently, we present an algorithmic framework which allows us to produce both fair and diverse samples. Our experimental results on an image summarization task show marked improvements in fairness without compromising feature diversity by much, giving us the best of both the worlds.

L. Elisa Celis, Amit Deshpande, Tarun Kathuria et al.

Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground set, they exhibit interesting properties such as negative correlation, and, unlike other models, have efficient algorithms for sampling. When applied to kernel methods in machine learning, DPPs favor subsets of the given data with more diverse features. However, many real-world applications require efficient algorithms to sample from DPPs with additional constraints on the subset, e.g., partition or matroid constraints that are important to ensure priors, resource or fairness constraints on the sampled subset. Whether one can efficiently sample from DPPs in such constrained settings is an important problem that was first raised in a survey of DPPs by \cite{KuleszaTaskar12} and studied in some recent works in the machine learning literature. The main contribution of our paper is the first resolution of the complexity of sampling from DPPs with constraints. We give exact efficient algorithms for sampling from constrained DPPs when their description is in unary. Furthermore, we prove that when the constraints are specified in binary, this problem is #P-hard via a reduction from the problem of computing mixed discriminants implying that it may be unlikely that there is an FPRAS. Our results benefit from viewing the constrained sampling problem via the lens of polynomials. Consequently, we obtain a few algorithms of independent interest: 1) to count over the base polytope of regular matroids when there are additional (succinct) budget constraints and, 2) to evaluate and compute the mixed characteristic polynomials, that played a central role in the resolution of the Kadison-Singer problem, for certain special cases.

L. Elisa Celis, Peter M. Krafft, Nathan Kobe

One goal of online social recommendation systems is to harness the wisdom of crowds in order to identify high quality content. Yet the sequential voting mechanisms that are commonly used by these systems are at odds with existing theoretical and empirical literature on optimal aggregation. This literature suggests that sequential voting will promote herding---the tendency for individuals to copy the decisions of others around them---and hence lead to suboptimal content recommendation. Is there a problem with our practice, or a problem with our theory? Previous attempts at answering this question have been limited by a lack of objective measurements of content quality. Quality is typically defined endogenously as the popularity of content in absence of social influence. The flaw of this metric is its presupposition that the preferences of the crowd are aligned with underlying quality. Domains in which content quality can be defined exogenously and measured objectively are thus needed in order to better assess the design choices of social recommendation systems. In this work, we look to the domain of education, where content quality can be measured via how well students are able to learn from the material presented to them. Through a behavioral experiment involving a simulated massive open online course (MOOC) run on Amazon Mechanical Turk, we show that sequential voting systems can surface better content than systems that elicit independent votes.